Priyanga Ganesan, UC San Diego
Quantum graphs are an operator space generalization of classical graphs that have appeared in different branches of mathematics including operator algebras, non-commutative topology and quantum information theory. In this talk, I will review the different perspectives to quantum graphs and introduce the spectrum associated with a quantum graph using the notion of a quantum adjacency matrix. It will be shown that many well-known bounds for chromatic number of classical graphs, such as Hoffman’s bound, also hold in the setting of quantum graphs. This is achieved using an algebraic characterization of quantum graph coloring and tools from operator algebra.